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On $2k$-Hitchin equations and Higgs bundles: a survey.
| Content Provider | Semantic Scholar |
|---|---|
| Author | Cardona, S. A. H. Compean, H. H. Garcia‐ Martinez-Merino, Aldo A. |
| Copyright Year | 2019 |
| Abstract | We study the $2k$-Hitchin equations introduced by Ward \cite{Ward 2} from the geometric viewpoint of Higgs bundles. After an introduction on Higgs bundles and $2k$-Hitchin equations, we review some elementary facts on complex geometry and Yang-Mills theory. Then we study some properties of holomorphic vector bundles and Higgs bundles and we review the Hermite-Yang-Mills equations and two related functionals to such equations. Using some geometric tools we show that, as far as Higgs bundles is concern, the $2k$-Hitchin equations are reduced to a set of only two equations. Finally, we introduce a functional closely related to the $2k$-Hitchin equations and we study some of its basic properties. |
| File Format | PDF HTM / HTML |
| Alternate Webpage(s) | https://arxiv.org/pdf/1912.00047v2.pdf |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
